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Some new refinement of Hermite-Hadamard type inequalities and their applications. (English) Zbl 1435.26024
Summary: In this paper first, we prove some new refinement of Hermite-Hadamard type inequalities for the convex function \(f\). Second, by using five new integral identities, we present some new Riemann-Liouville fractional trapezoid and midpoint type inequalities. Third, using these results, we present applications to \(f\)-divergence measures. At the end, some new bounds for special means of different positive real numbers and new error estimates for the trapezoidal and midpoint formula are provided as well. These results give us the generalizations and improvements of the earlier results.

MSC:
26D15 Inequalities for sums, series and integrals
26A33 Fractional derivatives and integrals
26A51 Convexity of real functions in one variable, generalizations
26D07 Inequalities involving other types of functions
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